AFM with Suppressed Parasitic Signals

ABSTRACT

An AFM that suppress parasitic deflection signals is described. In particular, the AFM may use a cantilever with a probe tip that is offset along a lateral direction from a longitudinal axis of torsion of the cantilever. During AFM measurements, an actuator may vary a distance between the sample and the probe tip along a direction approximately perpendicular to a plane of the sample stage in an intermittent contact mode. Then, a measurement circuit may measure a lateral signal associated with a torsional mode of the cantilever during the AFM measurements. This lateral signal may correspond to a force between the sample and the probe tip. Moreover, a feedback circuit may maintain, relative to a threshold value: the force between the sample and the probe tip; and/or a deflection of the cantilever corresponding to the force. Next, the AFM may determine information about the sample based on the lateral signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/US2017/15192, “AFM with Suppressed Parasitic Signals,” by OzgurSahin, filed on Jan. 26, 2017, the contents of which are hereinincorporated by reference.

FIELD

The described embodiments relate to a technique for performing AtomicForce microscopy (AFM) measurements with suppressed parasitic deflectionsignals.

RELATED ART

Scanning probe microscopy encompasses a wide range of imagingtechniques. During these imaging techniques, a probe in a scanning probemicroscope (SPM) interacts with a sample to generate a detectible signalthat corresponds to or is indicative of the interaction. In particular,the probe is often scanned across a surface of the sample to generateimages based on the detected signals from the probe. Typically, theprobes have very small physical dimensions to improve the resolution ofimages. In general, the images can reflect the topography and materialsproperties that vary across the surface.

AFM is a special type of SPM that uses the mechanical interaction of theprobe with the sample. In an AFM, the probe typically consists of aflexible cantilever beam (which is sometimes referred to as a‘cantilever’) with a sharp probe tip placed on one end. Deflections ofthe cantilever can be indicative of the forces between the probe tip andthe sample. These deflections are usually measured using a quadrantphoto-detector based on a laser beam that is reflected from the back ofthe cantilever.

Because of their ability to obtain high-resolution images under variousenvironmental conditions (including ambient and vacuum), AFMs haveproven to be versatile imaging instruments. Some AFMs generate an imageof the sample with the probe tip in contact with the sample surface.This imaging mode is commonly referred to as a ‘contact mode’. Inparticular, during the contact mode, the cantilever is typically broughtin contact with the sample surface and scanned across the sample. Then,a feedback system in the AFM monitors the deflection of the cantileverand adjusts the relative position of the cantilever with respect to thesample surface to maintain a constant deflection (which is sometimesreferred to as ‘set point deflection’). The relative adjustment signalsprovided by the feedback system can correspond to the surfacetopography, which may be represented in images. Because the cantileverdeflection in the contact mode is proportional to the forces exerted onthe probe tip and the sample, lower deflection set points are usuallydesirable in order to minimize damage to the probe tip and the sample.However, if the deflection set point is chosen too low, noise in the AFMdetection system and drifts in the measurement signals (e.g., because ofthermally induced changes in the cantilever shape) can preventacquisition of images.

Contact-mode AFM also offers the possibility to differentiate materialsforming the sample based on differences in their friction coefficients.For example, in lateral force microscopy, which is based on contact-modeAFM, torsional deflections of the cantilever caused by or associatedwith frictional forces can be detected to create an image that providescontrast indicative of the frictional characteristics of the samplesurface. Typically, the torsional deflection is detected from themeasurements signals provided by the quadrant photo-detector in the AFMdetection system, which can differentiate lateral and verticaldeflections of the cantilever. The lateral signal provided by thequadrant photo-detector is usually sensitive to the torsionaldeflections of the cantilever (around or about a longitudinal axis oftorsion) and the vertical signal at the quadrant photo-detector istypically sensitive to the flexural deflections of the cantilever.Because the cantilever is scanned across the surface while the probe tipis in continuous contact with the sample, frictional forces incontact-mode AFM can become significant and they can damage the probetip and the sample.

AFMs with intermittent contact modes, such as tapping-mode AFM, largelyovercome the limitation of the contact mode with respect to probetip-sample friction. For example, in tapping-mode AFM, the cantilever isusually vibrated at or near its resonance frequency and brought orplaced proximate the sample surface so that the vibrating probe tipmakes intermittent contact with the surface. The resulting intermittentinteraction reduces the probe-tip vibration amplitude. A feedbackmechanism typically adjusts the relative position of the cantilever withrespect to the surface in order to maintain the vibration amplitude at apredetermined set-point value. Because the intermittent contact reducesthe frictional forces, which can reduce damage to the probe tip and thesample, tapping-mode AFM has become among the most popular AFM imagingmodes.

In spite of the advantages of tapping-mode AFM, it can be difficult tooperate an AFM in the tapping mode because of the non-linear dynamics ofthe vibrating cantilever. In general, careful selection of the drivingforce, frequency, and set point amplitude are typically needed in orderto obtain good image quality. One approach for addressing the challengesassociated with the tapping mode and the imaging process is peak-forcetapping AFM. In peak-force tapping AFM, the distance between thecantilever and the sample is usually varied in an oscillatory orcyclical manner (which is sometimes referred to as ‘Z-modulation’).During the Z-modulation, the probe tip approaches, interacts, andretracts from the surface. Moreover, in this process the flexuraldeflection signals of the cantilever (which are provided by the quadrantphoto-detector) can allow substantially simultaneous determination ofthe probe tip-sample forces. Because the probe tip-sample forces aresubstantially instantaneously available with the probe-tip deflection,AFMs operating in peak-force tapping mode can use the peak value of theprobe tip-sample force interactions in each Z-modulation cycle tocontrol the feedback loop in the feedback system in order to track thetopography of the sample surface.

However, because of parasitic deflection signals in the peak-forcetapping AFM, measured instantaneous deflection signals often do notdirectly correspond to the instantaneous probe tip-sample forces. Notethat in the following discussion ‘parasitic deflection signals’ (whichare sometimes referred to as ‘parasitic signals’) are defined as themeasurement signals associated with operation of the AFM (e.g.,cantilever deflection associated with fluid drag, cantilever deflectionassociated with acceleration of the cantilever during the Z-modulation,thermal noise of the cantilever, and/or measurement-circuit noise,etc.). In order to address or correct for the parasitic signals, manypeak-force tapping AFMs perform a so-called ‘recovery step.’ During therecovery step, the AFM usually determines and subtracts parasiticdeflection signals from the detected deflection signals in order toobtain a deflection signal that is substantially free from parasiticsignals.

One recovery-step approach used for determining parasitic signals inpeak-force tapping AFM involves lifting the probe tip away from thesurface while turning the feedback off. By measuring the backgrounddeflection signals in the absence of probe tip-sample interactions, thisapproach can be used to determine the parasitic signals and subtract theparasitic signals from the detected deflection signals. Then, thefeedback can be turned on for imaging. While there are variations onthis basic approach for correcting the parasitic signals, the essentialfeature of this correction technique is that the background parasiticdeflection signals are determined when the probe tip is lifted away fromthe surface. However, the magnitude of some parasitic signals can changedepending on the position of the probe tip relative to the surface. Forexample, the magnitude of viscous drag typically varies with distancebetween the cantilever and the surface because of squeezed-film effects.Moreover, velocity-dependent drag forces usually change when the probetip makes contact with the surface because the probe-tip trajectory intime differs from a sinusoid. In contrast, when the cantilever is liftedto prevent interaction with the surface, the probe-tip trajectory intime is usually sinusoidal. Furthermore, there are often long-rangeprobe tip-sample interaction forces, which the recovery step mayinterpret as parasitic signals and, thus, which may be subtracted fromthe deflection signals.

These effects often limit the accuracy of the recovery step that is usedto subtract parasitic deflection signals. Because one of the primaryadvantages of peak-force tapping AFMs is the improved feedback controlbased on peak probe tip-sample forces, the inaccuracies in the recoverystep can limit the potential of peak-force tapping AFMs. For example,because of inaccurately determined parasitic signals, the recoveredprobe tip-sample forces can be larger or smaller than the actual probetip-sample forces. This error can limit the ability of a peak-forcetapping AFM to track the surface topography with low probe tip-sampleforces. Moreover, the inaccuracies can result in a loss of probetip-sample contact, or they can require the use of large forces that candamage the probe tip and/or the sample. In addition, inaccuratelydetermined probe tip-sample force waveforms can reduce the ability todetermine and image material properties of the sample, because thesemeasurements often use force-distance curves determined from probetip-sample forces and probe tip-sample distances.

Consequently, the difficult in accurately determining the parasiticdeflection signals can degrade the measurements performed using AFMs,and this can be frustrating to users.

SUMMARY

A first group of embodiments relate to an AFM. This AFM includes: asample stage that holds a sample; and a cantilever (or an AFMcantilever) with a probe tip that is offset along a lateral directionfrom a longitudinal axis of torsion of the cantilever. Moreover, the AFMmay include a first actuator that varies a distance between the sampleand the probe tip along a direction approximately perpendicular to aplane of the sample stage in an intermittent contact mode. Furthermore,the AFM may include a measurement circuit that measures a lateral signal(which is sometimes referred to as a ‘lateral deflection signal’)associated with a torsional mode of the cantilever during the AFMmeasurements, the lateral signal corresponding to a force between thesample and the probe tip. Additionally, the AFM may include a feedbackcircuit that maintains, relative to a threshold value: the force betweenthe sample and the probe tip; and/or a deflection of the cantilevercorresponding to the force. For example, the feedback circuit may changethe distance between the sample and the probe tip along the directionusing the first actuator and/or an optional second actuator (which maybe different from the first actuator). Note that the AFM may determineinformation about the sample based on the lateral signal.

In some embodiments, the measurement circuit measures a vertical signal(which is sometimes referred to as a ‘vertical deflection signal’)associated with relative displacement, along the direction, of the probetip and the sample.

Moreover, the AFM may further determine the information based on thevertical signal.

Furthermore, a contribution of parasitic signals to the information maybe reduced without the AFM performing a recovery operation or step, theparasitic signals may correspond to phenomena other than probetip-sample interaction, thermal noise of the cantilever andmeasurement-circuit noise, and the recovery operation may involveperforming measurements when the probe tip is other than in contact withthe sample.

Additionally, the information may include: the force between the sampleand the probe tip, topography of the sample, and/or a material propertyof the sample.

Note that the feedback circuit may maintain: a peak force, an averageforce during a gating interval, and/or a weighted average force duringthe gating interval.

In some embodiments, the variation of the distance has a fundamentalfrequency that is less than a flexural resonance frequency of thecantilever. For example, the fundamental frequency may be less than afrequency that corresponds to the flexural resonance frequency, such assignificantly less than a lowest flexural resonance frequency (and,thus, the AFM may not be operated in a tapping mode, which may involvedriving the cantilever at or near a flexural resonance frequency and theuse of the vibration amplitude as the feedback signal). Note that thefundamental frequency may be a lesser of: the flexural resonancefrequency divided by a square root of two, and the flexural resonancefrequency times one minus an inverse of two times a quality factor ofthe flexural resonance. However, in some embodiments, the fundamentalfrequency equals or is proximate to the flexural resonance frequency,and the AFM may operate in a tapping mode, however, with the feedbacksignal based on the peak force or an instantaneous force. In theseembodiments, the feedback signal may be derived or determined from thelateral signal.

Moreover, the AFM may include: a processor that executes a programmodule; and memory that stores the program module. When executed by theprocessor, the program module causes the AFM to operate in theintermittent contact mode and to determine the information.

Furthermore, a ratio of an offset of the probe tip along the lateraldirection to a cantilever body length may be greater than or equal to0.235 and/or a ratio of the offset to a cantilever body lateral widthmay be greater than or equal to 3.

Another embodiment provides a method for determining information aboutthe sample based on the lateral signal, which may be performed by theAFM.

Another embodiment provides a computer-readable storage medium thatstores a program module for use with the AFM When executed by the AFM,the program module causes the AFM to perform at least some of theaforementioned operations.

A second group of embodiments relate to an AFM. This AFM includes: asample stage that holds a sample; and a cantilever (or an AFMcantilever) with a probe tip that is offset along a lateral directionfrom a longitudinal axis of torsion of the cantilever. Moreover, the AFMmay include an actuator that varies a distance between the sample andthe probe tip along a direction approximately perpendicular to a planeof the sample stage in an intermittent contact mode. Furthermore, theAFM may include a measurement circuit that measures a lateral signalassociated with a torsional mode of the cantilever during the AFMmeasurements, and that measures a vertical signal associated withrelative displacement, along the direction, of the probe tip and thesample. Note that the lateral signal may correspond to a force betweenthe sample and the probe tip. Note that the AFM may determineinformation about the sample based on the lateral signal and thevertical signal.

Moreover, a contribution of parasitic signals to the information may bereduced without the AFM performing a recovery operation or step, theparasitic signals may correspond to phenomena other than probetip-sample interaction, thermal noise of the cantilever andmeasurement-circuit noise, and the recovery operation may involveperforming measurements when the probe tip is other than in contact withthe sample.

Furthermore, the information may include: the force between the sampleand the probe tip, topography of the sample, and/or a material propertyof the sample.

Additionally, the variation of the distance may have a fundamentalfrequency that is less than a flexural resonance frequency of thecantilever. For example, the fundamental frequency may be less than afrequency that corresponds to the flexural resonance frequency, such assignificantly less than a lowest flexural resonance frequency (and,thus, the AFM is not operated in a tapping mode, which may involvedriving the cantilever at or near a flexural resonance frequency and theuse of the vibration amplitude as the feedback signal). Note that thefundamental frequency may be a lesser of: the flexural resonancefrequency divided by a square root of two, and the flexural resonancefrequency times one minus an inverse of two times a quality factor ofthe flexural resonance. However, in some embodiments, the fundamentalfrequency equals or is proximate to the flexural resonance frequency,and the AFM may operate in a tapping mode, however, with the feedbacksignal based on the peak force or an instantaneous force.

In some embodiments, the AFM includes: a processor that executes aprogram module; and memory that stores the program module. When executedby the processor, the program module causes the AFM to operate in theintermittent contact mode and to determine the information.

Note that a ratio of an offset of the probe tip along the lateraldirection to a cantilever body length may be greater than or equal to0.235 and/or a ratio of the offset to a cantilever body lateral widthmay be greater than or equal to 3.

Moreover, the determination may involve correcting for parasitic signalsin the lateral signal and the vertical signal, the parasitic signalscorresponding to phenomena other than probe tip-sample interaction,thermal noise of the cantilever and measurement-circuit noise.

Another embodiment provides a method for determining information aboutthe sample, which may be performed by the AFM.

Another embodiment provides a computer-readable storage medium thatstores a program module for use with the AFM When executed by the AFM,the program module causes the AFM to perform at least some of theaforementioned operations.

A third group of embodiments provides an AFM cantilever for use with anAFM. This AFM cantilever includes: a cantilever body; and a probe tipthat is offset along a lateral direction from a longitudinal axis oftorsion of the cantilever. Moreover, the AFM cantilever may have atorsional mode that suppresses parasitic signals, the parasitic signalscorresponding to phenomena other than probe tip-sample interaction,thermal noise of the cantilever and measurement-circuit noise.

A fourth group of embodiments relates to an electronic device for usewith an AFM. This electronic device includes first input nodes thatcouple to a measurement circuit in the AFM and that receive, from themeasurement circuit, a measurement signal, where the measurement signalincludes a lateral signal associated with a torsional mode of acantilever in the AFM during AFM measurements, and the lateral signalcorresponds to a force between a sample and a probe tip in thecantilever. Moreover, the electronic device includes second input nodesthat couple to a feedback circuit in the AFM and that receive, from thefeedback circuit, a feedback signal, where the feedback signalcorresponds to a vertical signal associated with relative displacement,along a direction approximately perpendicular to a plane of the sample,of the probe tip and the sample. Furthermore, the electronic deviceincludes a signal-conditioning circuit that modifies the feedback signalso that the modified signal corresponds to a force between the sampleand the probe tip. Additionally, the electronic device includes firstoutput nodes that couple to the feedback circuit and that provide themeasurement signal to the feedback circuit, and second output nodes thatcouple to the measurement circuit and that provide the modified feedbacksignal to the measurement circuit.

Note that the signal-condition circuit may apply a feed-forwardmodification to the feedback signal.

Another embodiment provides a method for modifying a feedback signal,which may be performed by the electronic device.

Another embodiment provides a computer-readable storage medium thatstores a program module for use with the electronic device. Whenexecuted by the electronic device, the program module causes theelectronic device to perform at least some of the aforementionedoperations.

The preceding summary is provided as an overview of some exemplaryembodiments and to provide a basic understanding of aspects of thesubject matter described herein. Accordingly, the above-describedfeatures are merely examples and should not be construed as narrowingthe scope or spirit of the subject matter described herein in any way.Other features, aspects, and advantages of the subject matter describedherein will become apparent from the following Detailed Description,Figures, and Claims.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a block diagram illustrating an example of an atomic forcemicroscope (AFM) in accordance with an embodiment of the presentdisclosure.

FIG. 2 is a drawing illustrating an example of Z-modulation, a verticalsignal and a probe tip-sample force waveform as a function of time inaccordance with an embodiment of the present disclosure.

FIG. 3A is a drawing illustrating an example of a cantilever for usewith the AFM of FIG. 1 in accordance with an embodiment of the presentdisclosure.

FIG. 3B is a drawing illustrating an example of a cantilever for usewith the AFM of FIG. 1 in accordance with an embodiment of the presentdisclosure.

FIG. 4 is a drawing illustrating an example of vertical signal andparasitic-suppressed lateral signal measurements using the AFM of FIG. 1in accordance with an embodiment of the present disclosure.

FIG. 5A is a drawing illustrating an example of a vertical signal as afunction of time in accordance with an embodiment of the presentdisclosure.

FIG. 5B is a drawing illustrating an example of a lateral signal as afunction of time in accordance with an embodiment of the presentdisclosure.

FIG. 6 is a drawing illustrating an example a cantilever for use withthe AFM of FIG. 1 in accordance with an embodiment of the presentdisclosure.

FIG. 7 is a block diagram illustrating an example of a parasiticlateral-signal estimation circuit for use with the AFM of FIG. 1 inaccordance with an embodiment of the present disclosure.

FIG. 8 is a drawing illustrating an example of Z-modulation, a verticalsignal and a parasitic-suppressed lateral signal as a function of timein accordance with an embodiment of the present disclosure.

FIG. 9 is a drawing illustrating an example of a model of parasiticflexural deflections during Z-modulation of a cantilever in accordancewith an embodiment of the present disclosure.

FIG. 10 is a flow diagram illustrating an example of a method fordetermining information about a sample using the AFM of FIG. 1 inaccordance with an embodiment of the present disclosure.

FIG. 11 is a flow diagram illustrating an example of a method fordetermining information about a sample using the AFM of FIG. 1 inaccordance with an embodiment of the present disclosure.

FIG. 12 is a block diagram illustrating an example of an electronicdevice for use with an AFM in accordance with an embodiment of thepresent disclosure.

FIG. 13 is a flow diagram illustrating an example of a method formodifying a feedback signal using the electronic device of FIG. 12 inaccordance with an embodiment of the present disclosure.

FIG. 14 is a block diagram illustrating an example of an electronicdevice in accordance with an embodiment of the present disclosure.

Note that like reference numerals refer to corresponding partsthroughout the drawings. Moreover, multiple instances of the same partare designated by a common prefix separated from an instance number by adash.

DETAILED DESCRIPTION

In a first group of embodiments, an AFM that suppress parasiticdeflection signals is described. In particular, the AFM may use acantilever with a probe tip that is offset along a lateral directionfrom a longitudinal axis of torsion of the cantilever. During AFMmeasurements, an actuator may vary a distance between the sample and theprobe tip along a direction approximately perpendicular to a plane ofthe sample stage in an intermittent contact mode. Then, a measurementcircuit may measure a lateral signal associated with a torsional mode ofthe cantilever during the AFM measurements. This lateral signal maycorrespond to a force between the sample and the probe tip. Moreover, afeedback circuit may maintain, relative to a threshold value: the forcebetween the sample and the probe tip; and/or a deflection of thecantilever corresponding to the force. Next, the AFM may determineinformation about the sample based on the lateral signal.

In a second group of embodiments, an AFM that suppress parasiticdeflection signals is described. In particular, the AFM may use acantilever with a probe tip that is offset along a lateral directionfrom a longitudinal axis of torsion of the cantilever. During AFMmeasurements, an actuator may vary a distance between the sample and theprobe tip along a direction approximately perpendicular to a plane ofthe sample stage in an intermittent contact mode. Then, a measurementcircuit may measure a lateral signal associated with a torsional mode ofthe cantilever during the AFM measurements, and may measure a verticalsignal associated with relative displacement, along the direction, ofthe probe tip and the sample. The lateral signal may correspond to aforce between the sample and the probe tip. Next, the AFM may determineinformation about the sample based on the lateral signal and thevertical signal.

By suppressing the parasitic deflection signals, the measurementtechnique may improve probe tip-sample force measurement and controlduring AFM measurements (such as those that use peak force-basedfeedback). This capability may allow higher Z-modulation fundamentalfrequencies and, thus, faster imaging speeds (e.g., up to 10× faster)and improved image quality. For example, in AFMs that rely oninstantaneous probe tip-sample forces for feedback (such as themagnitude of peak forces), suppressing the parasitic deflection signalsmay allow topographic imaging with lower forces (such as lower peakforces). Moreover, because various sources of parasitic deflections(such as parasitic deflections due to viscous drag forces andaccelerations) depend on the vertical oscillation speed of thecantilever, by suppressing the parasitic deflection signals an AFM cantolerate faster oscillation speeds. Consequently, the measurementtechnique may allow larger Z-modulation fundamental frequencies and/oroscillation amplitudes than existing AFM measurement techniques withreduced parasitic signals. (Note that typical Z-modulation amplitudesmay be between 5 and 200 nm, but larger and smaller amplitudes can alsobe used.) The resulting shorter oscillation periods may reduce thefeedback delay. Therefore, suppressing the parasitic deflection signalscan be used to improve the imaging speed, i.e., to achieve a faster scanspeed or a faster tip-sample engagement process while keeping thetip-sample forces low. Furthermore, suppressing the parasitic deflectionsignals may eliminate the need for a recovery step or operation todetermine probe tip-sample forces. Additionally, the material propertiesand topology of the sample may be more accurately determined. Forexample, suppressing the parasitic deflection signals improves theaccurate probe tip-sample force waveforms, which can improve theaccuracy of mechanical property measurements based on force-distancecurves. Consequently, the measurement technique may provide moreflexible and accurate measurements, and may improve the user experiencewhen using the AFM.

We now describe embodiments of an AFM. FIG. 1 presents a block diagramillustrating an example of an AFM 100. This AFM may include: a samplestage 110 that holds a sample 112; a cantilever 114 with a probe tip 116that is offset along a lateral direction from a longitudinal axis oftorsion of the cantilever 114 (e.g., by more than 20 μm); an actuator118 (such as a piezoelectric element), coupled to sample stage 110and/or cantilever 114; and a measurement circuit 124 (including aquadrant detector); an optional feedback circuit 126 coupled tomeasurement circuit 124; and/or an optional actuator 128 coupled tosample stage 110 and/or cantilever 114. Note that optional feedbackcircuit 126 may be coupled to actuator 118 and/or an optional actuator128. AFM 100 may be used to perform measurements on a wide variety ofsamples, including: a biological sample, a polymer, a gel, a thin film,a patterned wafer, a data-storage device, an organic material, and/or aninorganic material. Moreover, the measurements may be performed inambient, liquid, aqueous buffers, or vacuum.

As described further below with reference to FIG. 14, AFM 100 mayinclude subsystems, such as a networking subsystem, a memory subsystemand a processor subsystem. For example, memory subsystem may store aprogram module that, when executed by the processor subsystem, causesAFM 100 to perform the measurement technique, which is described furtherbelow with reference to FIGS. 2-11. However, as described further belowwith reference to FIGS. 12-13, in some embodiments AFM 100 is used inconjunction with an electronic device (which is sometimes referred to asan ‘instrument module’), which facilitates the measurement technique.

As discussed previously, parasitic deflection signals, e.g., inpeak-force tapping AFM c(and, more generally, when Z-modulation is used,rather than driving the cantilever into flexural resonance, and when thefeedback relies on peak force, rather than oscillation amplitude), cancorrupt measurements of instantaneous deflection signals. Consequently,the instantaneous deflection signals may not directly correspond to theinstantaneous probe tip-sample forces.

In order to address this problem, actuator 118 may vary a distance 120,such that associated with translational motion, between sample 112 andprobe tip 116 along a direction 122 approximately perpendicular (such aswithin 15° of perpendicular) to a plane of sample stage 110 in anintermittent contact mode. (In addition, actuator 118 and/or a separatescanner, not shown, may scan probe tip 116 in a plane of sample 112 oralong a surface of sample 112 to generate an image.) For example,actuator 118 may vary a distance 120 or impart translational motionbetween sample 112 and cantilever 114 along a direction 122 usingZ-modulation (such as with modulation fundamental frequencies between250 and 1 kHz, 10 kHz or 20 kHz, and more generally using modulationfundamental frequencies that are typically below the lowest fundamentalflexural resonance frequency of cantilever 114), so that probe tip 116approaches, interacts with and moves away from the surface of sample112. (Note that this may be in contrast with tapping mode, in whichprobe tip 116 is moved by exciting a flexural motion of cantilever 114.However, in general during the measurement technique distance 120 mayvary because of translational motion and/or excitation of an excitationmode of cantilever 114.) In some embodiments, the variation of distance120 has a fundamental frequency that is less than a flexural resonancefrequency of cantilever 114, such as significantly less than a lowestflexural resonance frequency (i.e., cantilever 114 is operatedoff-resonance and, thus, AFM 100 may not be operated in a tapping mode,which typically involves driving the cantilever at or near a flexuralresonance frequency and the use of the vibration amplitude as thefeedback signal). Alternatively or additionally, the fundamentalfrequency may be less than a frequency that corresponds to the flexuralresonance frequency. However, in some embodiments, the fundamentalfrequency equals or is proximate to the flexural resonance frequency,and thus AFM 100 may be operated in tapping mode, however, with thefeedback signal based on the peak force or an instantaneous force. Notethat a torsional resonance frequency of cantilever 114 may be between 50kHz and several MHz.

Then, measurement circuit 124 may measure at least a torsionaldeflection signal associated with a torsional mode of cantilever 114during the AFM measurements. For example, if measurement circuit 124includes a laser and a position-sensitive quadrant photo-detector fordeflection detection of cantilever 114, measurement circuit 124 maymeasure at least a lateral signal associated with a torsional mode ofcantilever 114 during the AFM measurements, where the lateral signalcorresponds to a force between sample 112 and probe tip 116. (Note thatthe measured lateral signal in FIG. 1 is distinct from a so-called‘lateral force mode’ in which an AFM detects torsional motion associatedwith probe tip-sample frictional forces or plane forces. In themeasurement technique, the torsional deflections of cantilever 114 aredue to vertical forces and occur because probe tip 116 is offset alongthe lateral direction.)

Moreover, optional feedback circuit 126 (such as a proportional-integralcontroller) may maintain, relative to a threshold value (which issometimes referred to as ‘a set point value’): the force between sample112 and probe tip 116, and/or a deflection of cantilever 114corresponding to the force. For example, optional feedback circuit 126may maintain: a peak force as probe tip 116 interacts with sample 112,an average force during a gating interval as probe tip 116 interactswith sample 112, and/or a weighted average force during the gatinginterval as probe tip 116 interacts with sample 112. Furthermore, thepeak forces, average forces during the gating interval, and/or theweighted average force during the gating interval could be synchronouslyaveraged over many cycles of the fundamental frequency of the tiposcillation. Alternatively, the peak forces, average forces during thegating interval, and/or the weighted average force may be determinedfrom a synchronously averaged tip-sample force waveform at thefundamental frequency of the tip oscillation. The feedback may involveoptional feedback circuit 126, using actuator 118 and/or optionalactuator 128, changing distance 120 between sample 112 and probe tip 116along direction 122.

In some embodiments, optional feedback circuit 126 compares a verticalsignal from measurement circuit 124 to a threshold. The resultingdifference may be input to a proportional control, which outputs afeedback signal to actuator 118 and/or optional actuator 128. Ingeneral, the feedback may be based on the force and/or the deflectionmeasured vertical signal. Thus, the feedback signal may correspond to ormay be a function of the force and/or the deflection.

As discussed further below, optional feedback circuit 126 may use thepeak-force values (without or with reduced parasitic signals) determinedfrom torsional deflection signals to control a feedback loop, e.g., tomaintain a constant peak force at each cycle of Z-modulation and totrack the surface topography while scanning probe tip 116 over sample112. Thus, this measurement technique may maintain a steady stateinteraction by comparing the peak-force value to the set-point value andadjusting the relative distance 120 between probe tip 116 and sample 112based on the comparison, thereby tracking the surface of sample 112during the scanning process.

Note that, based on the torsional deflection signal or the lateralsignal, a contribution of parasitic signals to the peak-force values maybe reduced or eliminated without AFM 100 performing a recovery operationor step, i.e., without determining and subtracting the parasiticsignals. The parasitic signals may correspond to phenomena other thanprobe tip-sample interaction, thermal noise of cantilever 114 andmeasurement-circuit noise, and the recovery operation, which istypically performed in existing AFMs but may not be performed in themeasurement technique, may involve performing measurements when probetip 116 is other than in contact with sample 112 in order to determinethe parasitic signals or the contribution of the parasitic signals.Consequently, the measurement technique is sometimes referred to as a‘parasitic-suppressed AFM mode’ or a ‘psAFM mode’. In addition, thetorsional deflection signal or the lateral signal if a quadrantphoto-detector is used in the psAFM mode are sometimes, respectively,referred to as ‘parasitic-suppressed torsional deflection signals’ or‘parasitic-suppressed lateral signals.’ Therefore, this measurementtechnique may incorporate the advantages of using peak probe tip-sampleinteraction forces without the limitations of other AFM measurementtechniques and without performing the recovery operation or step. Notethat the measurement technique may be used for imaging with low forces(such as between 5 pN and 10 nN). However, the measurement technique maybe used with larger imaging forces, e.g., as large as 1 μN.

Instead of performing the recovery step or operation, AFM 100 may use abaseline torsional deflection value (or lateral deflection value) toadjust torsional deflection signals (or lateral signals). For example,because of misalignments in a laser position on a photo-detector inmeasurement circuit 124, there is typically a non-zero, baseline lateralsignal. This baseline lateral signal value can be subtracted frommeasured lateral signal so that lateral signals at the baseline areinterpreted as zero deflection and zero force. This may allow long-termimaging with low peak probe tip-sample forces. Moreover, because ofdrifts in AFM 100 (such as thermal drifts that cause cantilever 114 tobend and twist), the baseline can gradually and slowly change over time.Therefore, in some embodiments, AFM 100 determines the baseline lateralsignal repeatedly (such as periodically or after a time interval) toreadjust the detected parasitic-suppressed lateral signals. Note thatthe baseline lateral signal value can be determined from the value ofthe lateral signal when probe tip 116 is not interacting with thesurface of sample 112. However, this can be performed during normaloperation of AFM 100, as opposed to intentionally retracting probe tip116 away from the surface, as is typically the case in the recovery stepor operation.

(While the measurement technique allows the parasitic signals to bereduced or eliminated without the use of the recovery step or operation,in some embodiments the measurement technique includes a residualrecovery step or operation to estimate and subtract residual parasiticsignals in the parasitic-suppressed torsional deflection signals.Because these residual parasitic signals are small in magnitude,uncertainties in their determination can result in even smallerinaccuracies in the final deflection waveform. For example, AFM 100 may:lift probe tip 116 away from the surface of sample 112, measure thebackground signal, synthesize the background signal and subtract it fromthe parasitic-suppressed torsional deflection signals.)

Furthermore, AFM 100 may determine information about sample 112 based onthe lateral signal. For example, the information may include: the forcebetween sample 112 and probe tip 116, topography of sample 112, and/or amaterial property of sample 112 (such as an elastic modulus, astiffness, a work of adhesion, a peak adhesive force, another adhesionmetric, a loss modulus, a storage modulus, a hardness, an electricalproperty, an optical property, etc.). As discussed above, by reducing oreliminating the contribution of the parasitic signals, AFM 100 maydetermine the informationwithout AFM 100 performing the recoveryoperation or step.

In order to determine the electrical property or characteristic, AFM 100may apply a DC or AC voltage signal to probe tip 116 relative to sample112, so that the measured forces from the parasitic-suppressed torsionaldeflection signals contain information about the electrical propertiesof the surface of sample 112, which can be used to determine electricalproperties of the surface. By scanning cantilever 114 across the surfaceof sample 112, these measurements can be used to generate images thatmap electrical properties of materials, such as the dielectric constant,the resistivity, the electrical impedance, etc.

Moreover, in order to determine an optical property or characteristic,AFM 100 may apply an electromagnetic pulse, an infrared pulse or anoptical pulse to probe tip 116 and/or sample 112, so that rapidtopographic changes associated with absorption of the pulse can bedetected from the parasitic-suppressed torsional deflections. Bysuppressing parasitic signals, the measurement technique may improve theability of AFM 100 to detect small and rapid changes in surface heightin response to the absorption. This is because the variations in thesurface height may result in a change in the probe tip-sample force,which may cause a change in the parasitic-suppressed torsionaldeflection signal. Furthermore, because the absorption characteristicsof sample 112 depends on its chemical composition, the measurementtechnique may improve the ability to detect chemical changes and also tomap the chemical composition of sample 112 with nanometer-scaleresolution. Note that, in order to enhance the sensitivity of themeasurement technique, the timing of the pulse(s) may be matched withthe duration of the probe tip-sample contact during Z-modulation. Thetemporal width and/or intensity of a pulse can be adjusted to maximizethe contrast. By detecting and recording changes in theparasitic-suppressed torsional deflections in response to the appliedpulse(s) and scanning cantilever 114 across the surface of sample 112,it may be possible to map the chemical composition of sample 112.

In some embodiments, measurement circuit 124 measures a vertical signalassociated with relative displacement, along direction 122, of sample112 and probe tip 116. This vertical signal is sometimes referred to asa ‘flexural signal’ or a ‘flexural deflection signal.’ Moreover, AFM 100may also further determine the information based on the vertical signal.

For example, AFM 100 may generate at least one force-distance curve and,more generally, at least one force-distance curve at each pixel locationof an image. The force values may be determined from theparasitic-suppressed torsional deflection signals, and the distancevalues may be determined from the displacement of actuator 118 used forthe Z-modulation and the flexural deflection signals. The force-distancecurves can be used to measure one or more materials properties. Byscanning cantilever 114 across the surface of sample 112, these measuredquantities can be used to generate images that map composition ofmaterials, which is particularly useful in characterization ofheterogeneous materials. Note that the vertical signals may be measuredand used in conjunction with the lateral signals to adjust the distancevalues because of the position of probe tip 116. In particular, this isbecause the actual position of probe tip 116 relative to the surface isthe sum of tip displacements due to flexural and torsional motions, aswell as the displacement of actuator 118 used for Z-modulation.Moreover, note that the measurement technique may reduce theuncertainties introduced by the recovery step or operation that is oftenused to remove the parasitic signals.

In addition to correcting the lateral signals for the baseline lateralsignal value, AFM 100 may perform an adjustment to minimize the effectsof angular misalignment between the orientation of cantilever 114 andthe orientation of the photo-detector in measurement circuit 124. Ifthis angular misalignment is large, it can exacerbate crosstalk fromflexural deflections into the lateral signals. Therefore, AFM 100 mayperform an adjustment to minimize the angular misalignment, such as byadjusting the photo-detector orientation. Alternatively or additionally,AFM 100 may determine the amount of crosstalk (such as by comparing thevertical signal and the lateral signal from cantilever 114 when it isnot interacting with sample 112), and then correcting for the crosstalk.

While the preceding embodiment included the use of feedback (viaoptional feedback circuit 126, actuator 118 and/or optional actuator128), in other embodiments the information is determined without the useof feedback. In particular, measurement circuit 124 may measure thelateral signal and the vertical signal. Then, AFM 100 may determine theinformation about sample 112 based on the lateral signal and thevertical signal. Moreover, the determination may involve correcting forparasitic signals in the lateral signal and the vertical signal. Theparasitic signals may correspond to phenomena other than probetip-sample interaction, thermal noise of cantilever 114 andmeasurement-circuit noise.

Although we describe AFM 100 as an example, in alternative embodiments,different numbers or types of components may be present. For example,some embodiments comprise more or fewer components. Alternatively oradditionally, two or more components may be combined together.Therefore, in some embodiments actuator 118 and optional actuator 128are combined into a single actuator. However, in other embodiments,actuator 118 and/or optional actuator 128 are separate actuators. Theremay also be additional actuators (not shown) that are more efficient athigher frequencies.

We now further describe the measurement technique. Peak-force-based AFMsoften provide improved control of the imaging process. In particular,instead of relying on the vibration amplitude (as is usually the case intapping-mode AFMs), the peak-force value can offer a robust techniquefor detecting probe tip-sample contact. However, parasitic deflectionsignals can degrade the performance of peak-force-based AFMs by makingit difficult to accurately determine probe tip-sample forces.

FIG. 2 presents a drawing illustrating an example of Z-modulation, avertical signal and a probe tip-sample force waveform as a function oftime for a peak-force tapping AFM operating in liquid. As shown in FIG.2, the Z-modulation signal is often sinusoidal with a fundamentalfrequency and amplitude.

In general, the probe tip-sample force waveform is usually not directlydetectible from the measured vertical deflections. In particular, theprobe tip-sample force waveform typically exhibits an alternatingpattern of attractive and repulsive forces varying around a baselinevalue. Moreover, the vertical signal may not follow a clear pattern thatcan directly reveal the probe tip-sample forces. Instead, there isusually a background signal in addition to the deflection signals thatare generated in response to the probe tip-sample forces. In FIG. 2,arrows indicate regions 210 where the probe tip-sample interactionoccurs. In this example, the value of the deflection signal in one ofthese regions is below the peak vertical signal. Therefore, unless probetip-sample forces are high enough to cause deflection above thebackground, it may not be possible to directly use the peak verticalsignal for feedback control.

Note that the background signals may be parasitic signals that originatefrom the operation of the AFM (such as from sources other than probetip-sample interactions). For example, the parasitic signals can includecantilever bending due to viscous drag forces, acceleration due toZ-modulation, and/or laser interference. The parasitic signals areusually oscillatory signals, primarily at the fundamental frequency ofthe Z-modulation. Moreover, parasitic signals due to laser interferencemay exhibit frequency doubling. (In this definition, noise from thethermally induced vibrations of the cantilever and photo-detector noisemay not be parasitic signals). In addition to the parasitic signals,there may be additional signals due to the excitation of cantileverresonances in response to abruptly changing adhesion forces. Theseparasitic signals, which are often encountered when imaging takes placein air due to strong capillary forces, are sometimes referred to as'unwanted signals.' This is because the unwanted signals distort thecantilever deflection signals and can make it difficult to relatedeflection signals to probe tip-sample forces.

As noted previously, in order to obtain deflection signals that are freefrom parasitic signals, existing peak-force tapping AFMs typicallyemploy a recovery step or operation. This recovery step may be performedby a digital controller that includes an analog-to-digital converter, afield programmable gate array (FPGA), and/or a digital signal processor.For example, a background signal associated with AFM operation may bedetermined by lifting the probe tip up from the surface. Once thebackground signal is determined, a background generator may synthesize acorrection signal that is then subtracted from the detected deflectionsignal. In addition, existing AFMs may use another operation todetermine baseline signals associated with drifts in cantileverdeflection and laser position on the photo-detector. This baseline forcemay be treated separately from parasitic signals. Note that this otheroperation may be performed so that the zero deflection signal of thebaseline-corrected signal corresponds to zero probe tip-sample force.

In contrast, the measurement technique may suppress parasitic signals(e.g., by more than an order of magnitude) so that probe tip-sampleforces can be detected more accurately for use in peak force feedbackand to facilitate more accurate measurements of materials properties. Inparticular, the AFM cantilever may respond to vertical probe tip-sampleforces by torsional bending (i.e., twisting). Then, during theZ-modulation, torsional deflections of the cantilever may result indeflection signals in which parasitic signals are suppressed relative tothe signals that are in response to the probe tip-sample forces.

FIGS. 3A and 3B presents drawings illustrating an example of a T-shapedcantilever 300 for use with AFM 100 (FIG. 1) that strongly respond tovertical probe tip-sample forces by torsional bending. In particular,FIG. 3A illustrates a torsional mode of cantilever 300 and FIG. 3Billustrates a flexural mode of cantilever 300.

FIG. 4 presents a drawing illustrating an example of vertical signal andparasitic-suppressed lateral signal measurements provided by a quadrantphoto-detector in peak-force-based AFM 100 (FIG. 1) with a T-shapedcantilever. During Z-modulation, the relative distance between thecantilever and the sample may be modulated using an actuator, so thatthe probe tip approaches, interacts, and moves away from the samplesurface. Deflections of the cantilever in flexural and torsional modesmay be detected by the position-sensitive quadrant photo-detector. Inparticular, the lateral signal from the photo-detector may correspond tothe torsional bending of the cantilever, and the vertical signal maycorrespond to the flexural bending of the cantilever. Moreover, thelaterally offset position of the probe tip may cause torsional bendingin response to vertical probe tip-sample forces. Furthermore, thecantilever may respond to the probe tip-sample forces by bending in theflexural mode. Therefore, both the vertical and lateral signals mayconvey or include information about the probe tip-sample forces.However, parasitic signals may be suppressed in the lateral signals. Incontrast with the vertical signals, the lateral signals may facilitatethe detection of peak forces, as well as in detecting the entire probetip-sample force waveform.

FIG. 5A presents a drawing illustrating an example of a vertical signal510 as a function of time. This vertical signal may correspond toflexural bending of a T-shaped cantilever (with the probe tip laterallyoffset from the longitudinal axis of torsion) in a peak-force-based AFMwhile interacting with a sample. Moreover, FIG. 5B presents a drawingillustrating an example of a lateral signal 512 as a function of time.This lateral signal may correspond to torsional bending of the T-shapedcantilever in the peak-force-based AFM while interacting with a sample.In FIGS. 5A and 5B, parasitic signals 514 and 516 are shown as dashedlines. Note that parasitic signals 514 and 516 may be estimated byfitting to a sinusoidal waveform. (Alternatively, parasitic signals 514may be estimated by lifting the cantilever away from the surface usingthe recovery step or operation.) In some embodiments, the fittingprocess excludes the contact zone, which is approximately 40% of theZ-modulation period in this example.

Note that peak-to-peak parasitic deflection 518 is substantially largerthan vertical signal 510 corresponding to peak force 520. In contrast,peak-to-peak parasitic deflection 522 is substantially less than lateralsignal 512 due to peak probe tip-sample force 524. Consequently, byusing lateral signal 512 instead of vertical signal 510, parasiticsignal 516 is substantially suppressed relative to lateral signal 512 inresponse to peak probe tip-sample force 524. Therefore, in themeasurement technique lower probe tip-sample forces can be detectedwithout using a recovery step or operation. Stated differently, whilethe same probe tip-sample force generates both vertical and lateralsignals 510 and 512, lateral signal 512 rises well above parasiticsignal 516 in the lateral channel and vertical signal 510 remains belowparasitic signal 514 in the vertical channel. Thus, imaging can beperformed with lower probe tip-sample forces without the need for arecovery step or operation.

FIG. 6 presents a drawing illustrating an example of a cantilever 600for use with AFM 100 (FIG. 1). This cantilever includes a cantileverbody 610 having: a length 612, a stem or lateral width 614, an armlength 616, an arm width 618, a reflector width 620 and a reflectorlength 622. Moreover, cantilever 600 may include a probe tip 624 that isoffset 626 along a lateral direction 628 from a longitudinal axis oftorsion 630 of cantilever 600. Note that cantilever 600 may have atorsional mode that suppresses parasitic signals, where the parasiticsignals correspond to phenomena other than probe tip-sample interaction,thermal noise of the cantilever and measurement-circuit noise.Therefore, cantilever 600 may be used to measure parasitic-suppressedtorsional deflection signals.

The geometry of cantilever 600 may reduce the parasitic signals andforce noise in peak-force-based AFMs without significantly compromisingnoise performance (e.g., without increasing thermal noise). For example,as a non-limiting example, length 612 may be 115 μm, lateral width 614may be 9 μm, arm length 616 may be 60 μm, arm width 618 may be 9 μm,reflector width 620 may be 20 μm, reflector length 622 may be 25 μm andoffset 626 may be greater than 2 μm (such as 20-30 μm, e.g., 27 μm).Note that offset 626 is intentional and, therefore, is larger thanaccidental offsets than can occur due to fabrication errors such as maskmisalignment. Such unintentional offsets are typically less than 2 μm.

In some embodiments, a ratio of offset 626 of probe tip 624 alonglateral direction 628 to a length 612 of cantilever body 610 (which issometimes referred to as an ‘aspect ratio’) is greater than or equal to0.235 or is greater than or equal to 0.4. The aspect ratio may impactthe ratio of the torsional spring constant to the flexural springconstant. Note that the spring constants in the torsional and flexuralmodes each refer to ratio of the force acting on probe tip 624 to thedisplacement of probe tip 624 in the respective mode. (In general,probe-tip displacement is a superposition of displacements in severalflexural and torsional modes, with the dominant ones being the modeswith the lowest flexural and torsional resonance frequencies,respectively.) In general, the larger the aspect ratio, the lower thetorsional spring constant relative to the flexural spring constant.Therefore, cantilever 600 may have a larger aspect ratio to achievelower torsional spring constants. In some embodiments, the torsionalspring constant is decreased by reducing a thickness of cantilever 600.However, this change may also reduce the flexural spring constant, whichmay make it difficult for probe tip 624 to detach from the samplesurface as the cantilever moves away from the sample. In addition, alower flexural spring constant can cause a large parasitic signal in thevertical channel. Consequently, the aspect ratio may be used to reducethe torsional spring constant without compromising the performance ofcantilever 600 with respect to the suppression of the parasitic signals.

Moreover, a ratio of offset 626 to lateral width 614 of cantilever body610 (which is sometimes referred to as ‘an offset-to-stem ratio’) may begreater than or equal to 3. This geometry of cantilever 600 may offerreduced surface area for the same lateral offset 626 and length 612). Areduced surface area may result in lower fluid drag forces, whilemaintaining a high aspect ratio to keep the torsional spring constantlow relative to the spring constant of the fundamental flexural mode.Lower fluid drag forces may reduce: parasitic deflections in theflexural mode; crosstalk from the vertical signal to the lateral signal;and/or the thermal-noise-limited minimum detectible force. Thesecapabilities may allow peak forces to be detected accurately. In thisregard, arm width 618, reflector width 620 and reflector length 622 mayalso be small. In general, the reflector area may be sufficiently largeto accommodate a laser spot of the AFM If the AFM has a sufficientlysmall laser spot size, the reflector area may be as narrow as lateralwidth 614. In embodiments where the cantilever edges are not straightlines (so that the lateral width cannot be determined clearly), theaverage lateral width (i.e., the average width in lateral direction 628)can be used. Because the narrowest regions dominate the torsional springconstant, the averaging may be performed over the regions along length612 of cantilever 600 whose widths belong to the lowest 50% of thewidths along length 612. If there are multiple stems that are connectedto the arm that holds probe tip 624 or the reflector area, the width maybe calculated as the total width in lateral direction 628 (i.e., the sumover the stems).

Furthermore, the torsional spring constant of the fundamental flexuralmodes of cantilever 600, which may be defined as the ratio of the forceacting on probe tip 624 and along a direction that is perpendicular tothe cantilever surface (such as the surface that reflects the laserlight used for deflection detection) to the probe-tip displacementcaused by torsional deflections, may be between 0.01 and 10,000 N/m. Asnoted previously, if cantilever 600 has a spring constant that is toolow (lower than about 0.01 N/m), it may be difficult to break probetip-sample contact due to adhesive forces. In addition, if cantilever600 has spring constant that is too high (higher than about 1,000 N/m),it may be difficult to maintain a low enough peak force during theimaging process. The wide range of spring constants of cantilever 600may provide the capability to measure and map mechanical properties overa wide range, from 100 Pa to 100 GPa. The lower range may be smallerthan the value in existing peak-force tapping AFMs that rely on arecovery step or operation to obtain deflection signals. Thus,cantilever 600 may make it possible to detect probe tip-sample forcewaveforms on more compliant samples, which may be difficult to measureaccurately due to difficulties in the recovery step or operation.

Additionally, cantilever body 610 may include silicon and/or siliconnitride, and probe tip 624 may include silicon, silicon dioxide anddiamond. Cantilever 600 may extend from a support structure (not shown)at base 632 of cantilever body 610. Moreover, as a non-limiting example,cantilever body 610 may have a thickness of approximately 600 nm.Furthermore, there may be a gold coating having an approximate thicknessof 30 nm on a back surface of cantilever body 610 (facing away fromprobe tip 624) to enhance reflectivity of the laser beam used indeflection detection. Cantilever 600 may be manufactured using a varietyof lithographic fabrication techniques, including additive andsubtractive processes. Note that probe tip 624 may be chemicallyfunctionalized to alter probe tip-sample interaction forces, e.g., toreduce or enhance capillary forces and/or electrical forces.

As shown in FIG. 6, cantilever 600 may have a T-shape (in addition tothe lateral displacement of probe tip 624). However, in otherembodiments another geometry may be used to provide parasitic-suppressedtorsional deflection signals. In particular, cantilever 600 may have ageometry in which probe tip-sample interaction forces generatesufficient torsional deflection signals to exceed the parasitic signals.In general, the suitability of a particular cantilever geometry forsuppressing parasitic signals can be tested in a peak-force tapping AFM(e.g. using vertical signals to determine peak forces for feedbackcontrol) and comparing the lateral and vertical signals. If themagnitude of the parasitic signal is smaller than the magnitude of thelateral signal associated with the peak probe tip-sample force (comparedto the relative magnitude of the vertical signal), then this cantilevergeometry may provide parasitic-suppressed torsional deflection signals.Note that such cantilevers are sometimes referred as‘parasitic-suppressed torsional cantilevers.’

Note that longitudinal axis of torsion 630 may refer to an axis of thecantilever 600 where cantilever 600 is not displaced by torsionalvibration when cantilever 600 is vibrate, i.e., the axis of torsion iswhere cantilever 600 does not move in the torsional mode. Morespecifically, the axis of torsion generally extends in longitudinaldirection 634 of cantilever 600. For a symmetrical cantilever, such asrectangular cantilever 600, the axis of torsion is the centerline ofcantilever body 610 perpendicular to base 632 of cantilever 600.However, for a cantilever having a different geometry, the axis oftorsion may not necessarily be the centerline of the cantilever bodyand/or may not be a straight line. Moreover, depending of the placementof probe tip 624, deflection signals corresponding to a positive probetip-sample force (pointing away from the sample surface towards theprobe) can have a positive or negative value. For example, probe tip 624may be placed on the left side of longitudinal axis of torsion 630instead of the right side (as shown in FIG. 6), which would causecantilever 600 to twist in the opposite direction in response to probetip-sample forces. In the present disclosure, the convention is thatpositive (repulsive) probe tip-sample forces cause positive torsionaldeflection signals.

As discussed previously, in addition to using a parasitic-suppressedtorsional cantilever to image a sample (including varying the distancebetween the cantilever and the sample surface so that the probe tipapproaches, interacts and moves away from the surface, and measuringvertical and/or lateral signals in which the parasitic signals aresuppressed by the torsional mode of the cantilever), the measurementtechnique may include a residual recovery operation to estimate andremove residual parasitic signals in the parasitic-suppressed torsionaldeflection signals.

This is shown in FIG. 7, which presents a block diagram illustrating anexample of a parasitic lateral-signal estimation circuit 700 for usewith AFM 100 (FIG. 1). In particular, parasitic lateral signal estimator710 may use parasitic-suppressed torsional deflection signal 712 toestimate residual parasitic signal 714 in the lateral signals. Theestimation operation may include separating the probe tip from thesample while feedback is turned off, measuring the deflection signals inthe separated configuration, synthesizing a signal that replicates themeasured signals (i.e., residual parasitic signal 714), subtracting thesynthesized signal from the detected signals, and turning he feedback onto bring the probe tip back into contact with the sample. In parasiticlateral-signal estimation circuit 700, subtraction circuit 716 maysubtract residual parasitic signal 714 from parasitic-suppressedtorsional deflection signal 712 to obtain a lateral signal 718 that haslower contribution from parasitic signals, resulting in furtherimprovements in the detection of probe tip-sample forces. The resultingtorsional deflection or lateral signal 718 may be used for feedback in apeak-force-based AFM.

Note that the removal of residual parasitic signal 714 in theparasitic-suppressed torsional deflection signal 712 (the aforementionedresidual recovery operation) may not be needed for peak-force-basedfeedback control when parasitic-suppressed torsional signal 712 are usedto determine the peak forces. This is because the parasitic signals mayalready be suppressed substantially, and therefore very small probetip-sample forces are sufficient to overcome feedback errors introducedby the remaining parasitic signals. However, removal of residualparasitic signals can further improve force-distance curve measurements,which may be used to measure materials properties, such as: adhesion,elasticity, Young's modulus, and/or dissipation.

In some embodiments, an analog approach is used to reduce crosstalk inthe measurement technique. In particular, residual parasitic signal 714in parasitic-suppressed torsional deflection signal 712 can include acrosstalk signal from the vertical signal into the lateral signal. Whilethe residual recovery operation can be used to estimate and remove aresidual parasitic signal associated with the crosstalk, separately oradditionally the crosstalk may be eliminated using a calibrationoperation. For example, the crosstalk may be minimized by adjusting therelative orientation of the quadrant photo-detector. In particular,after applying a Z-modulation signal (while the probe tip is separatedfrom the sample), the orientation of the photo-detector may be adjustedto minimize the magnitude of the lateral signal. (Alternatively, thisadjustment may be performed electronically.) Because the relativeorientation of the cantilever can affect the degree of crosstalk, thiscalibration operation may be performed after placing a new cantilever inan AFM.

Alternatively or additionally, in some embodiments a digital approach isused to reduce crosstalk in the measurement technique. In particular,while the probe tip is separated from the sample, a Z-modulation signalcan be applied, and vertical and lateral detector signals can beanalyzed digitally to determine the crosstalk ratio. The crosstalk ratiomay be determined by subtracting the respective baseline deflectionsfrom each of the vertical and lateral signals. Then, the scalar ratiocan be determined based on a linear fit between the resulting lateralsignal and the resulting vertical signal (e.g., by using a least-squaresfitting technique). Once the crosstalk ratio is determined, the lateralsignal may be redefined to account for the crosstalk. For example, theinstantaneous vertical signal may be divided by the crosstalk ratio, andthen the result may be subtracted from the raw lateral signal to obtaina redefined lateral signal. The redefined lateral signal may also be aparasitic-suppressed torsional deflection signal and its parasiticcomponent may have a lower contribution from crosstalk. Note that theZ-modulation signal may have the fundamental frequency that will be usedduring the measurement and imaging processes, because the magnitude ofthe crosstalk may depend on the modulation frequency (e.g., differentflexural modes can have different crosstalk ratios and the fundamentalfrequency of the Z-modulation can affect the relative contributions fromeach flexural mode to the overall cantilever motion). Therefore, thedegree of crosstalk can be minimized while engaging the probe tip to thesample. In some embodiments, the crosstalk ratio is calculated using afield-programmable gate array (FPGA), and the redefined lateral signalis determined from the raw vertical and lateral detector signals usingan FPGA. Unlike the residual recovery operation, the calibrationoperation may reduce the crosstalk independent of the Z-modulationamplitude, because the crosstalk ratio may be substantially independentof the Z-modulation amplitude.

Another approach for estimating the crosstalk ratio during the imagingprocess involves determining the ratio of the baseline-correctedvertical signal to the baseline-corrected parasitic-suppressed torsionaldeflection signal using signals that are outside of predeterminedintervals (which are sometimes referred to as ‘interaction windows’)that approximate the duration of the probe tip-sample interaction duringZ-modulation. This is shown in FIG. 8, which presents a drawingillustrating an example of Z-modulation 810, a vertical signal 812 and aparasitic-suppressed lateral signal 814 as a function of time. Thepredetermined intervals 816 may be chosen to be 40% of the period ofZ-modulation 810 and they can be centered on a time that corresponds tothe peak force value (prior to the subtraction of the residual forces).In compliant regions of samples, the predetermined interval can bechosen to be longer to ensure that the probe tip-sample forces areexcluded from the calculation of the crosstalk ratio. Moreover, thecrosstalk ratio may be estimated at the beginning of a scanning processduring imaging of a sample, and it can be updated using measurements ofthe vertical and lateral signals during the imaging process. Once thecrosstalk ratio is determined, the baseline-corrected vertical signalscan be divided by the crosstalk ratio and the result can be subtractedfrom the baseline-corrected parasitic-suppressed torsional deflectionsignals to obtain the redefined lateral signals.

In some embodiments, the AFM estimates and subtracts the residualparasitic signals and/or determines the crosstalk ratio and theredefined lateral signals using one or more analog-to-digital (A/D)converters, one or more digital signal processors, and/or one or moreFPGAs. By performing the calculations digitally, rapid feedback may beprovided based on the peak deflection or force value.

Note that peak-force-based AFMs typically offer improved control andfaster feedback relative to tapping-mode AFMs. In contrast withpeak-force-based AFMs, tapping-mode AFMs usually rely on changes in thevibration amplitude for feedback, which often exhibit complicateddynamics and slow transients. In peak-force-based AFMs, as soon as thevalue of peak force is determined, the feedback signal can be adjustedbefore the oscillation cycle is completed. The feedback loop may use anactuator (such as a piezoelectric actuator) to adjust the relativeposition of the cantilever and the sample so that the peak force isrestored to its set point value in the subsequent cycles of the periodicZ-modulation. Because peak forces are typically encountered when the tipis at its lowest point in its trajectory, the measured value of theparasitic-suppressed torsional deflection signal at this point can beused as the peak force signal. Therefore, A/D converter(s), digitalfiltering, baseline subtraction, and/or background generation andsubtraction can be used with the parasitic-suppressed torsionaldeflection signals from an AFM operating in peak-force tapping-mode(i.e., by relying on the lateral signal rather than the vertical signalto obtain peak probe tip-sample forces). Note that because the parasiticsignals are greatly suppressed in the measurement technique, a recoverystep or operation may not be necessary. In addition, additionaltechniques for determining the feedback control signal (such as apredetermined synchronization distance and/or gated averaging) may beused with the parasitic-suppressed torsional deflection signals.

While the peak force value may be used in the feedback loop, forcevalues at any other time point within the Z-modulation cycle can beused. In these embodiments, the center point of the gating interval(i.e., the time window used to determine the peak force value, such asby averaging forces during the gating interval) may be adjusted to adesired time point. Furthermore, rather than averaging the signalswithin the gating interval, it is also possible to apply a weightedaverage. The use of gated averaging may allow exclusion of time pointsat which the probe tip-sample forces are not substantially larger thannoise (e.g., thermal noise) and/or the parasitic deflections. Moreover,the weighted averaging can be used to give larger weights to the timepoints at which the measured forces are larger than other time pointswithin the gating interval. Furthermore, weighted averaging of otherfunctions of the probe tip-sample force waveform (such as the differencebetween the maximum and minimum force values) can also be used for thefeedback.

While force is the physical quantity representing the interactionbetween the probe tip and the sample, for the purpose of feedbackdeflection signals can also be used directly, without determining acalibrated force value. For example, the feedback loop can maintain apeak deflection signal during the imaging process. Alternatively oradditionally, parasitic-suppressed torsional deflection signals at othertime points within the Z-modulation cycle or a weighted averaging ofdeflection signals can also be used.

In some embodiments, the parasitic signals in the parasitic-suppressedtorsional signals result from crosstalk from the vertical signals. Thesevertical signals may be due to acceleration as a result of theZ-modulation, fluid-drag forces and/or unwanted excitation of slowlydecaying fundamental flexural resonance. The parasitic signals may bereduced by only moving the sample for Z-modulation. This is because, ifthe cantilever is being moved for Z-modulation (e.g., while keepingsample fixed in the Z direction perpendicular or approximatelyperpendicular to the sample surface), the actuator may excite resonancesif the fundamental frequency is at or near the resonance frequency of aflexural mode. However, many AFMs are equipped with actuators that movethe cantilever in the Z direction. This configuration may allowsimultaneous imaging using optical microscopy and AFM. In order tofurther suppress the parasitic signals associated with crosstalk intotorsional deflection signals, in an AFM that moves the cantilever forZ-modulation, the modulation fundamental frequency may be less than thefundamental flexural resonance frequency of the cantilever.Alternatively, resonance effects may dominate the probe-tip displacement(and, therefore, the parasitic flexural deflection signals) when theZ-modulation fundamental frequency is within the resonance peak definedby the quality factor of the cantilever. Therefore, the Z-modulation maybe kept below the resonance peak. (Choosing a modulation fundamentalfrequency above the resonance peak may result in the cantilever movingin the opposite direction or out of phase, which may enhance theflexural deflection signal, and therefore the parasitic signals in thelateral deflections due to crosstalk.) Note that the boundaries of theresonance peak can be determined from measurements of the fundamentalflexural resonance frequency and its quality factor (such as using thethermal noise spectrum). The frequency at which the cantilever response(such as the amplitude of the thermal noise, or the vibration amplitudeif frequency tuning is used) is half of its peak value at the resonancefrequency may be the lower boundary of the resonance peak. If theresonance frequency and quality factor of the cantilever are known, thelower bound of the resonance peak can be calculated according to:

${f_{low} = {f_{res} - \frac{f_{res}}{2\; Q}}},$

where f_(low) is the lower bound of the resonance peak, f_(res) is theflexural resonance frequency of the cantilever measured in the imagingfluid, and Q is the quality factor of the fundamental flexural mode.(Note that the parameters may be measured in the imaging medium and inthe vicinity of the sample to account for squeezed-film dampingeffects.) For example, if the resonance frequency of the cantilever is50 kHz and its Q is 25, then the lower bound is 49 kHz. In this example,the drive or modulation fundamental frequency may be below 49 kHz.

In embodiments that move the sample during the Z-modulation, there maybe a benefit in using a Z-modulation fundamental frequency that is belowthe resonance peak because viscous drag forces can mechanically couplethe sample to the cantilever. This effect may be weaker than the effectin embodiments in which the cantilever is moved during the Z-modulation,because acceleration-related excitation of cantilever movements may beprevented.

Although choosing a Z-modulation fundamental frequency below theresonance peak may reduce the crosstalk signals associated with theparasitic excitation of a flexural resonance, choosing an even lowerZ-modulation fundamental frequency may keep acceleration-relatedparasitic flexural deflection of the cantilever small. This isillustrated in FIG. 9, which presents a drawing of an example of a model900 of parasitic flexural deflections during Z-modulation of acantilever. In particular, the fundamental flexural mode of thecantilever can be approximated by a damped simple harmonic oscillator(higher-order modes typically have high resonance frequencies and springconstants, and their effects in this analysis are typically negligible).The actuator used for the Z-modulation may move the cantilever base atan angular frequency w. However, while the cantilever body mayaccelerate according to the base displacement, the probe-tip trajectory(the position versus time curve) may not be identical to the basedisplacement. In the frequency domain, the equation of motion of theprobe-tip mass (e.g., the equation of motion corresponding to theequivalent mass in the simple harmonic oscillator model), which relatesthe displacement of the probe tip to the displacement of the cantileverbase, may be expressed as:

${X = \frac{A}{\left( {1 - \frac{w^{2}}{w_{o}^{2}}} \right) - \frac{j \cdot w}{Q \cdot w_{o}}}},$

where X and A are the frequency-dependent complex (having real andimaginary parts) values corresponding to the probe-tip displacement andcantilever-base displacement (i.e., X and A are the Fourier transformsof the time-dependent displacements), w is the fundamental frequency ofZ-modulation, w₀ and Q are the resonance frequency and quality factor ofthe fundamental flexural mode in the medium of imaging, and j is theimaginary unit (i.e., the square root of −1). In order to ensure thatthe cantilever-base displacement dominates the probe-tip displacement(i.e., the parasitic flexural deflections induced by the Z-modulationare less than Z-modulation distance of the base), X and A may beconstrained according to

|X−A|<|A|.

In this inequality, the left side is the magnitude of the parasiticflexural deflections and the right side is the magnitude of thecantilever-base modulation distance. Therefore, in order to dominate theprobe-tip displacement, the cantilever-base displacement may have tohave a larger magnitude than the parasitic flexural deflections. Usingthe frequency-dependent relationship between X and A, it can be shownthat, in order for the above inequality to hold, the Z-modulationfundamental frequency may be less than a threshold frequency,f_(threshold), i.e.,

$f_{threshold} = {\frac{f_{res}}{\sqrt{2}}.}$

Consequently, in order to ensure that the Z-modulation distance at thecantilever base dominates the probe-tip displacement, the modulationfundamental frequency may be below the threshold frequency(approximately 0.707 times the resonance frequency of the fundamentalflexural mode in the imaging medium).

Note that we defined two frequency values (f_(low) and f_(threshold)) toensure that parasitic signals in the torsional deflection signals arenot increased by parasitic flexural deflections via crosstalk ofsignals. Depending on the quality factor of the fundamental flexuralresonance frequency, one or the other frequency value may be smaller.The lower of the two frequency values, which may be defined as thecritical frequency f_(critical), may be used in the measurementtechnique.

In embodiments that use fundamental frequencies at or near a flexuralresonance frequency of the cantilever, an analog or a digital techniquefor crosstalk elimination may be used. By reducing the parasitic signalsin the lateral signal, these embodiments may allow the use offundamental frequencies such as those that are used in the tapping mode,while using the parasitic-suppressed torsional deflection signals (i.e.,the lateral signal) to obtain the feedback signal. In these embodiments,the feedback signal may be based on a peak force, an average forceduring a gating interval, and/or a weighted average force during agating interval. Furthermore, these forces may be synchronously averagedover many cycles of the fundamental frequency of the tip oscillation.Alternatively, the peak forces, average forces during the gatinginterval, and/or the weighted average force may be determined from asynchronously averaged tip-sample force waveform at the fundamentalfrequency of the tip oscillation. By relying on peak forces during theimaging process, this approach may offer faster feedback and more robustoperation, in comparison to existing tapping-mode AFM measurementtechniques.

We now describe embodiments of a method in the measurement technique.FIG. 10 presents a flow diagram illustrating an example of a method 1000for determining information about a sample based on a lateral signalusing an AFM, such as AFM 100 (FIG. 1). During operation, the AFM mayvary a distance between the sample and a probe tip (operation 1010)along a direction approximately perpendicular to a plane of the samplein an intermittent contact mode, where the probe tip is included in acantilever and is offset along a lateral direction from a longitudinalaxis of torsion of the cantilever. Then, the AFM may measure the lateralsignal (operation 1012) associated with a torsional mode of thecantilever during AFM measurements, where the lateral signal correspondsto a force between the sample and the probe tip;

Moreover, the AFM may maintain, using a feedback circuit in the AFM andrelative to a threshold value, a parameter (operation 1014), such as:the force between the sample and the probe tip, and/or a deflection ofthe cantilever corresponding to the force. Note that maintaining theforce may involve changing the distance between the sample and the probetip along the direction.

Next, the AFM may determine the information about the sample (operation1016) based on at least the lateral signal.

As noted previously, in some embodiments the measurement technique isused without feedback. This is shown in FIG. 11, which presents a flowdiagram illustrating an example of a method 1100 for determininginformation about a sample using an AFM, such as AFM 100 (FIG. 1).During operation, the AFM may vary a distance between the sample and aprobe tip (operation 1110) along a direction approximately perpendicularto a plane of the sample in an intermittent contact mode, where theprobe tip is included in a cantilever and is offset along a lateraldirection from a longitudinal axis of torsion of the cantilever.

Then, the AFM may measure a lateral signal (operation 1112) associatedwith a torsional mode of the cantilever during AFM measurements and maymeasure a vertical signal (operation 1114) associated with relativedisplacement, along the direction, of the probe tip and the sample,where the lateral signal corresponding to a force between the sample andthe probe tip.

Next, the AFM may determine the information about the sample (operation1116) based on the lateral signal and the vertical signal. For example,the information may include material properties derived from forcecurves obtained using the lateral signal and the vertical signal duringZ-modulation (such as from force-distance curves). In some embodiments,the information may include a mapping of other aspects of the probetip-sample interaction, such as: the indentation distance, energydissipation (the area inside the force curve), and/or electricalproperties if a voltage signal is applied to the probe tip relative tothe sample.

In some embodiments, an electronic device (which is sometimes referredto as an ‘instrument module’) is used in conjunction with an AFM (whichmay be an existing AFM) and a parasitic-suppressed torsional cantileverto perform the measurement technique. FIG. 12 presents a block diagramillustrating an example of an electronic device 1200 for use with anAFM, such as AFM 100 (FIG. 1). This electronic device may include inputnodes 1210 that couple to a measurement circuit in the AFM and thatreceive, from the measurement circuit, a measurement signal, where themeasurement signal includes a lateral signal associated with a torsionalmode of a cantilever in the AFM during AFM measurements, and the lateralsignal corresponds to a force between a sample and a probe tip in thecantilever. Moreover, electronic device 1200 may include input nodes1212 that couple to a feedback circuit in the AFM and that receive, fromthe feedback circuit, a feedback signal, where the feedback signalcorresponds to a vertical signal associated with relative displacement,along a direction approximately perpendicular to a plane of the sample,of the probe tip and the sample. Furthermore, electronic device 1200 mayinclude a signal-conditioning circuit 1214 that modifies the feedbacksignal so that the modified signal corresponds to a force between thesample and the probe tip. Additionally, electronic device 1200 mayinclude output nodes 1216 that couple to the feedback circuit and thatprovide the measurement signal to the feedback circuit, and output nodes1218 that couple to the measurement circuit and that provide themodified feedback signal to the measurement circuit. Note thatsignal-condition circuit 1214 may apply a feed-forward modification tothe feedback signal, which, in part, may be based on a transfer functionand/or desired signal conditioning. Thus, electronic device 1200 mayprovide a deliberately different or modified feedback signal to the AFMThis may overcome a speed limitation of the AFM

Thus, electronic device 1200 may facilitate process theparasitic-suppressed torsional deflection signal (i.e., the lateralsignal) and to provide the AFM with one or more signals including, butnot limited to: a feedback error signal, values of materials properties,and/or a waveform derived from the parasitic-suppressed torsionaldeflection (such as a derived deflection waveform).

In some embodiments, electronic device 1200 receives, from the AFM, oneor more additional signals, including: a vertical signal, a Z-modulationsignal, signals containing information about the relative position ofthe sample and the probe tip, an optional electrical bias applied to theprobe tip and/or the sample, and/or a trigger signal for electromagneticand optical pulses applied to the tip and/or the sample. In general, theinput signal to and output signals from electronic device 1200 can beanalog and/or digital signals.

Note that electronic device 1200 may include one or more processors ormicro-controllers, one or more FPGAs, and/or one or more A/D convertersthat can sample the vertical and lateral signals. The processor(s)and/or FPGAs can use the digitized signals from the A/D converter(s) toprocess the parasitic-suppressed torsional deflection signal. Theprocessing can include operations such as: determining a crosstalkratio, obtaining redefined lateral signals from the crosstalk ratio,and/or determining and removing a residual parasitic signal. Moreover,the processing may include filtering and scaling of signals.Furthermore, electronic device 1200 may include one or moredigital-to-analog (D/A) converters so that calculated signals can beconverted to analog signals.

In some embodiments, electronic device 1200 is interfaced with the AFMsuch that the feedback error signal calculated by electronic device 1200(e.g., based on the peak force or peak deflection signal) can replacethe original feedback error signal of the AFM. Alternatively oradditionally, electronic device 1200 may be interfaced with the AFM suchthat the waveform calculated by electronic device 1200 (e.g., a deriveddeflection waveform) can be directly used by the AFM feedback circuit orcontroller. In this way, the AFM may process the calculated waveformsignal to determine its own feedback signal. Note that electronic device1200 may include additional inputs and/or outputs dedicated tocommunicate with a computer or workstation (which may be included in orseparate from the AFM) to transfer data and to adjust settings oftechniques used by the processor(s) and/or the FPGAs.

The preceding apparatuses may include fewer or additional components,the positions of one or more components may be moved two or morecomponents may be combined into a single component and/or a singlecomponent may be separated into two or more separate components. Forexample, electronic device 1200 may include: scaling amplifiers, summingamplifiers, filters, and/or an analog sample-and-hold circuit thatsamples the deflection signal at a predetermined synchronizationdistance (such as the synchronization distance that is set to the timewhen peak forces are observed). The synchronization distance can bedetermined from the Z-modulation signal input to electronic device 1200and/or using a peak-detection circuit that processes theparasitic-suppressed torsional signal. Moreover, the output of thesample-and-hold circuit can be provided as one of the outputs ofelectronic device 1200 to the AFM feedback circuit or controller to beused as the feedback signal. Furthermore, electronic device 1200 mayoutput a signal waveform that is a linearly scaled version of theparasitic-suppressed torsional deflection signal, and the AFM may usethis waveform to determine the feedback signal used for tracking thesurface topography. Additionally, electronic device 1200 may directlyprovide the parasitic-suppressed torsional deflection signal to the AFMfor use in determining the feedback signal. In these embodiments,electronic device 1200 may essentially swap the vertical signal with theparasitic-suppressed torsional signal or the lateral signal.

FIG. 13 is a flow diagram illustrating an example of a method 1300 formodifying a feedback signal using an electronic device, such aselectronic device 1200 (FIG. 12). During operation, the electronicdevice may receive, on first input nodes from a measurement circuit inan AFM, a measurement signal (operation 1310), where the measurementsignal includes a lateral signal associated with a torsional mode of acantilever in the AFM during AFM measurements, and the lateral signalcorresponds to a force between a sample and a probe tip in thecantilever. Moreover, the electronic device may receive, on second inputnodes from a feedback circuit in the AFM, a feedback signal (operation1312), where the feedback signal corresponds to a vertical signalassociated with relative displacement, along a direction approximatelyperpendicular to a plane of the sample, of the probe tip and the sample.

Then, the electronic device may modify, using a signal-conditioningcircuit, the feedback signal (operation 1314) so that the modifiedsignal corresponds to a force between the sample and the probe tip. Forexample, the signal-condition circuit may apply a feed-forwardmodification to the feedback signal.

Furthermore, the electronic device may provide, on first output nodes,the measurement signal (operation 1316) to the feedback circuit.Additionally, the electronic device may provide, on second output nodes,the modified feedback signal (operation 1318) to the measurementcircuit.

In some embodiments of methods 1000, 1100 and/or 1300, there may beadditional or fewer operations. Moreover, the order of the operationsmay be changed, and/or two or more operations may be combined into asingle operation. For example, in method 1300, instead of receiving thefeedback signal as an input, in some embodiments the signal-conditioningcircuit computes the feedback signal based on the measurement signal andprovides it to the feedback circuit in the AFM.

We now describe embodiments of an electronic device. FIG. 14 presents ablock diagram illustrating an example of an electronic device 1400, suchas AFM 100 in FIG. 1. This electronic device includes processingsubsystem 1410, memory subsystem 1412, networking subsystem 1414,measurement subsystem 1426 and/or optional feedback subsystem 1432.Processing subsystem 1410 includes one or more devices configured toperform computational operations. For example, processing subsystem 1410can include one or more microprocessors, one or more GPUs, one or moreapplication-specific integrated circuits (ASICs), one or moremicrocontrollers, one or more programmable-logic devices (such asFPGAs), and/or one or more digital signal processors (DSPs).

Memory subsystem 1412 includes one or more devices for storing dataand/or instructions for processing subsystem 1410 and networkingsubsystem 1414. For example, memory subsystem 1412 can include dynamicrandom access memory (DRAM), static random access memory (SRAM), and/orother types of memory. In some embodiments, instructions for processingsubsystem 1410 in memory subsystem 1412 include: one or more programmodules or sets of instructions (such as program module 1422 oroperating system 1424), which may be executed by processing subsystem1410. Note that the one or more computer programs may constitute acomputer-program mechanism. Moreover, instructions in the variousmodules in memory subsystem 1412 may be implemented in: a high-levelprocedural language, an object-oriented programming language, and/or inan assembly or machine language. Furthermore, the programming languagemay be compiled or interpreted, e.g., configurable or configured (whichmay be used interchangeably in this discussion), to be executed byprocessing subsystem 1410.

In addition, memory subsystem 1412 can include mechanisms forcontrolling access to the memory. In some embodiments, memory subsystem1412 includes a memory hierarchy that comprises one or more cachescoupled to a memory in electronic device 1400. In some of theseembodiments, one or more of the caches is located in processingsubsystem 1410.

In some embodiments, memory subsystem 1412 is coupled to one or morehigh-capacity mass-storage devices (not shown). For example, memorysubsystem 1412 can be coupled to a magnetic or optical drive, asolid-state drive, or another type of mass-storage device. In theseembodiments, memory subsystem 1412 can be used by electronic device 1400as fast-access storage for often-used data, while the mass-storagedevice is used to store less frequently used data.

Networking subsystem 1414 includes one or more devices configured tocouple to and communicate on a wired and/or wireless network (i.e., toperform network operations), including: control logic 1416, an interfacecircuit 1418, one or more antennas 1420 and/or input/output (I/O) port1430. (While FIG. 14 includes one or more antennas 1420, in someembodiments electronic device 1400 includes one or more nodes 1408,e.g., a pad, which can be coupled to one or more antennas 1420. Thus,electronic device 1400 may or may not include one or more antennas1420.) For example, networking subsystem 1414 can include a Bluetoothnetworking system, a cellular networking system (e.g., a 3G/4G/5Gnetwork such as UMTS, LTE, etc.), a universal serial bus (USB)networking system, a networking system based on the standards describedin IEEE 802.11 (e.g., a Wi-Fi networking system), an Ethernet networkingsystem, and/or another networking system.

Networking subsystem 1414 includes processors, controllers,radios/antennas, sockets/plugs, and/or other devices used for couplingto, communicating on, and handling data and events for each supportednetworking system. Note that mechanisms used for coupling to,communicating on, and handling data and events on the network for eachnetwork system are sometimes collectively referred to as a ‘networkinterface’ for the network system. Moreover, in some embodiments a‘network’ between the electronic devices does not yet exist. Therefore,electronic device 1400 may use the mechanisms in networking subsystem1414 for performing simple wireless communication between the electronicdevices, e.g., transmitting advertising or beacon frames and/or scanningfor advertising frames transmitted by other electronic devices.

Measurement subsystem 1426 may include a parasitic-suppressed torsionalcantilever, a driver or an actuator, a laser and/or quadrantphoto-detector to perform the measurement technique. Thus, measurementsubsystem 1426 may determine the lateral signal and/or the verticalsignal. Moreover, optional feedback subsystem 1432 may use at least thelateral signal in a feedback-control loop.

In some embodiments, electronic device 1400 includes a display subsystem(not shown) for displaying information on a display, which may include adisplay driver and the display, such as a liquid-crystal display, amulti-touch touchscreen, etc. For example, the display may display animage acquired during a scan of a sample.

Within electronic device 1400, processing subsystem 1410, memorysubsystem 1412, networking subsystem 1414, measurement subsystem and/oroptional feedback subsystem may be coupled together using bus 1428. Bus1428 may include an electrical, optical, and/or electro-opticalconnection that the subsystems can use to communicate commands and dataamong one another. Although only one bus 1428 is shown for clarity,different embodiments can include a different number or configuration ofelectrical, optical, and/or electro-optical connections among thesubsystems.

Electronic device 1400 can be (or can be included in) any electronicdevice with at least one network interface. For example, electronicdevice 1400 can be (or can be included in): a desktop computer, a laptopcomputer, a subnotebook/netbook, a server, a tablet computer, asmartphone, a cellular telephone, a smartwatch, a consumer-electronicdevice, a portable computing device, an AFM, another measurement deviceand/or another electronic device.

Although specific components are used to describe electronic device1400, in alternative embodiments, different components and/or subsystemsmay be present in electronic device 1400. For example, electronic device1400 may include one or more additional processing subsystems, memorysubsystems, networking subsystems, measurement subsystems, feedbacksubsystems, display subsystems and/or signal-processing subsystems (suchas A/D converters or D/A converters). Additionally, one or more of thesubsystems may not be present in electronic device 1400. Moreover, insome embodiments, electronic device 1400 may include one or moreadditional subsystems that are not shown in FIG. 14. Also, althoughseparate subsystems are shown in FIG. 14, in some embodiments, some orall of a given subsystem or component can be integrated into one or moreof the other subsystems or component(s) in electronic device 1400. Forexample, in some embodiments program module 1422 is included inoperating system 1424.

Moreover, the circuits and components in electronic device 1400 may beimplemented using any combination of analog and/or digital circuitry,including: bipolar, PMOS and/or NMOS gates or transistors. Furthermore,signals in these embodiments may include digital signals that haveapproximately discrete values and/or analog signals that have continuousvalues. Additionally, components and circuits may be single-ended ordifferential, and power supplies may be unipolar or bipolar.

An integrated circuit may implement some or all of the functionality ofelectronic device 1400. Moreover, the integrated circuit may includehardware and/or software components that are used for performing atleast some of the operations in the measurement technique.

While AFM is used as an illustrative example of the measurementtechnique, the described embodiments of the measurement technique may beused in a variety of measurement devices. Furthermore, while some of theoperations in the preceding embodiments were implemented in hardware orsoftware, in general the operations in the preceding embodiments can beimplemented in a wide variety of configurations and architectures.Therefore, some or all of the operations in the preceding embodimentsmay be performed in hardware, in software or both. For example, at leastsome of the operations in the measurement technique may be implementedusing program module 1422, operating system 1424, a driver for interfacecircuit 1418 and/or in firmware in a hardware component in electronicdevice 1400 (such as firmware in interface circuit 1418). Alternativelyor additionally, at least some of the operations in the measurementtechnique may be implemented in a physical layer, such as hardware ininterface circuit 1418.

In the preceding description, we refer to ‘some embodiments.’ Note that‘some embodiments’ describes a subset of all of the possibleembodiments, but does not always specify the same subset of embodiments.Moreover, note that the numerical values provided are intended asillustrations of the measurement technique. In other embodiments, thenumerical values can be modified or changed.

The foregoing description is intended to enable any person skilled inthe art to make and use the disclosure, and is provided in the contextof a particular application and its requirements. Moreover, theforegoing descriptions of embodiments of the present disclosure havebeen presented for purposes of illustration and description only. Theyare not intended to be exhaustive or to limit the present disclosure tothe forms disclosed. Accordingly, many modifications and variations willbe apparent to practitioners skilled in the art, and the generalprinciples defined herein may be applied to other embodiments andapplications without departing from the spirit and scope of the presentdisclosure. Additionally, the discussion of the preceding embodiments isnot intended to limit the present disclosure. Thus, the presentdisclosure is not intended to be limited to the embodiments shown, butis to be accorded the widest scope consistent with the principles andfeatures disclosed herein.

What is claimed is:
 1. An atomic force microscope (AFM), comprising: asample stage configured to hold a sample; a cantilever with a probe tip,the probe tip being offset along a lateral direction from a longitudinalaxis of torsion of the cantilever; a first actuator, coupled to at leastone of the sample stage and the cantilever, configured to vary adistance between the sample and the probe tip along a directionapproximately perpendicular to a plane of the sample stage in anintermittent contact mode; a measurement circuit configured to measure alateral signal associated with a torsional mode of the cantilever duringthe AFM measurements, the lateral signal corresponding to a forcebetween the sample and the probe tip, wherein, during the AFMmeasurements, the variation of the distance has a fundamental frequencythat is significantly less than a lowest flexural resonance frequency ofthe cantilever; and a feedback circuit, coupled to the measurementcircuit and one of the first actuator and a second actuator, configuredto maintain, relative to a threshold value, one of: the force betweenthe sample and the probe tip, and a deflection of the cantilevercorresponding to the force, wherein the second actuator is configured tochange the distance between the sample and the probe tip along thedirection, and wherein the AFM is configured to determine informationabout the sample based on the lateral signal.
 2. The AFM of claim 1,wherein the measurement circuit is configured to measure a verticalsignal associated with relative displacement, along the direction, ofthe probe tip and the sample.
 3. The AFM of claim 1, wherein the AFM isfurther configured to further determine the information based on thevertical signal.
 4. The AFM of claim 1, wherein a contribution ofparasitic signals to the information is reduced without the AFMperforming a recovery operation; wherein the parasitic signalscorresponding to phenomena other than probe tip-sample interaction,thermal noise of the cantilever and measurement-circuit noise; andwherein the recovery operation involves performing measurements when theprobe tip is other than in contact with the sample.
 5. The AFM of claim1, wherein the information includes one of: the force between the sampleand the probe tip, topography of the sample, and a material property ofthe sample.
 6. The AFM of claim 1, wherein the feedback circuit isconfigured to maintain one of: a peak force, an average force during agating interval, and a weighted average force during the gatinginterval.
 7. The AFM of claim 1, wherein the fundamental frequency is alesser of: the flexural resonance frequency divided by a square root oftwo, and the flexural resonance frequency times one minus an inverse oftwo times a quality factor of a flexural resonance of the cantilever. 8.The AFM of claim 1, wherein the AFM further comprises: a processor,coupled to the measurement circuit and at least one of the firstactuator and the second actuator, configured to execute a programmodule; and memory, coupled to the processor, configured to store theprogram module, wherein the program module, when executed by theprocessor, causes the AFM to operate in the intermittent contact modeand to determine the information.
 9. The AFM of claim 1, wherein a ratioof an offset of the probe tip along the lateral direction to acantilever body length is greater than or equal to 0.235 and a ratio ofthe offset to a cantilever body lateral width is greater than or equalto
 3. 10. The AFM of claim 1, wherein the first actuator is differentfrom the second actuator.
 11. A method for determining information abouta sample based on a lateral signal, comprising: varying a distancebetween the sample and a probe tip along a direction approximatelyperpendicular to a plane of the sample in an intermittent contact mode,wherein the probe tip is included in a cantilever and is offset along alateral direction from a longitudinal axis of torsion of the cantilever,and wherein the variation of the distance has a lowest fundamentalfrequency that is significantly less than a lowest flexural resonancefrequency of the cantilever; measuring the lateral signal associatedwith a torsional mode of the cantilever during atomic force microscopy(AFM) measurements, the lateral signal corresponding to a force betweenthe sample and the probe tip; maintaining, using a feedback circuit inthe AFM and relative to a threshold value, one of: the force between thesample and the probe tip, and a deflection of the cantilevercorresponding to the force, wherein maintaining the force involveschanging the distance between the sample and the probe tip along thedirection, and determining the information about the sample based on thelateral signal.
 12. The method of claim 11, wherein the method furthercomprises: measuring a vertical signal associated with relativedisplacement, along the direction, of the probe tip and the sample; anddetermining the information is further based on the vertical signal. 13.The method of claim 11, wherein a contribution of parasitic signals tothe information is reduced without performing a recovery operation;wherein the parasitic signals corresponding to phenomena other thanprobe tip-sample interaction and thermal noise of the cantilever andnoise associated with a detector that measures the lateral signal; andwherein the recovery operation involves performing measurements when theprobe tip is other than in contact with the sample.
 14. The method ofclaim 11, wherein the feedback circuit maintains one of: a peak force,an average force during a gating interval, and a weighted average forceduring the gating interval.
 15. The method of claim 11, wherein thefundamental frequency is a lesser of: the flexural resonance frequencydivided by a square root of two, and the flexural resonance frequencytimes one minus an inverse of two times a quality factor of a flexuralresonance of the cantilever.
 16. A non-transitory computer-readablestorage medium for use in conjunction with an atomic force microscope(AFM), the computer-readable storage medium configured to store aprogram module that, when executed by the AFM, causes the AFM to: vary adistance between a sample and a probe tip along a directionapproximately perpendicular to a plane of the sample in an intermittentcontact mode, wherein the probe tip is included in a cantilever and isoffset along a lateral direction from a longitudinal axis of torsion ofthe cantilever, and wherein the variation of the distance has afundamental frequency that is significantly less than a lowest flexuralresonance frequency of the cantilever; measure a lateral signalassociated with a torsional mode of the cantilever during atomic forcemicroscopy (AFM) measurements, the lateral signal corresponding to aforce between the sample and the probe tip; maintain, using a feedbackcircuit in the AFM and relative to a threshold value, one of: the forcebetween the sample and the probe tip, and a deflection of the cantilevercorresponding to the force, wherein maintaining the force involveschanging the distance between the sample and the probe tip along thedirection, and determine information about the sample based on thelateral signal.
 17. The computer-readable storage medium of claim 16,wherein, when executed by the AFM, the program module causes the AFM to:measure a vertical signal associated with relative displacement, alongthe direction, of the probe tip and the sample; and determine theinformation further based on the vertical signal.
 18. Thecomputer-readable storage medium of claim 16, wherein a contribution ofparasitic signals to the information is reduced without performing arecovery operation; wherein the parasitic signals corresponding tophenomena other than probe tip-sample interaction and thermal noise ofthe cantilever and noise associated with a detector that measures thelateral signal; and wherein the recovery operation involves performingmeasurements when the probe tip is other than in contact with thesample.
 19. The computer-readable storage medium of claim 16, whereinthe feedback circuit maintains one of: a peak force, an average forceduring a gating interval, and a weighted average force during the gatinginterval.
 20. The computer-readable storage medium of claim 16, whereinthe fundamental frequency is a lesser of: the flexural resonancefrequency divided by a square root of two, and the flexural resonancefrequency times one minus an inverse of two times a quality factor ofthe flexural resonance.
 21. An atomic force microscope (AFM),comprising: a sample stage configured to hold a sample; a cantileverwith a probe tip, the probe tip being offset along a lateral directionfrom a longitudinal axis of torsion of the cantilever; an actuator,coupled to at least one of the sample stage and the cantilever,configured vary a distance between the sample and the probe tip along adirection approximately perpendicular to a plane of the sample stage inan intermittent contact mode; a measurement circuit configured tomeasure a lateral signal associated with a torsional mode of thecantilever during the AFM measurements, and configured to measure avertical signal associated with relative displacement, along thedirection, of the probe tip and the sample, wherein the lateral signalcorresponding to a force between the sample and the probe tip, andwherein, during the AFM measurements, the variation of the distance hasa fundamental frequency that is significantly less than a lowestflexural resonance frequency of the cantilever; and wherein the AFM isconfigured to determine information about the sample based on thelateral signal and the vertical signal.
 22. The AFM of claim 21, whereina contribution of parasitic signals to the information is reducedwithout the AFM performing a recovery operation; wherein the parasiticsignals corresponding to phenomena other than probe tip-sampleinteraction, thermal noise of the cantilever and measurement-circuitnoise; and wherein the recovery operation involves performingmeasurements when the probe tip is other than in contact with thesample.
 23. The AFM of claim 21, wherein the information includes oneof: the force between the sample and the probe tip, topography of thesample, and a material property of the sample.
 24. The AFM of claim 21,wherein the fundamental frequency is a lesser of: the flexural resonancefrequency divided by a square root of two, and the flexural resonancefrequency times one minus an inverse of two times a quality factor ofthe flexural resonance.
 25. The AFM of claim 21, wherein the AFM furthercomprises: a processor, coupled to the measurement circuit and theactuator, configured to execute a program module; and memory, coupled tothe processor, configured to store the program module, wherein theprogram module, when executed by the processor, causes the AFM tooperate in the intermittent contact mode and to determine theinformation.
 26. The AFM of claim 21, wherein a ratio of an offset ofthe probe tip along the lateral direction to a cantilever body length isgreater than or equal to 0.235.
 27. The AFM of claim 21, wherein a ratioof the offset to a cantilever body lateral width is greater than orequal to
 3. 28. The AFM of claim 21, wherein the determination involvescorrecting for parasitic signals in the lateral signal and the verticalsignal, the parasitic signals corresponding to phenomena other thanprobe tip-sample interaction, thermal noise of the cantilever andmeasurement-circuit noise.
 29. A method for determining informationabout a sample, comprising: varying a distance between the sample and aprobe tip along a direction approximately perpendicular to a plane ofthe sample in an intermittent contact mode, wherein the probe tip isincluded in a cantilever and is offset along a lateral direction from alongitudinal axis of torsion of the cantilever, and wherein thevariation of the distance has a fundamental frequency that issignificantly less than a lowest flexural resonance frequency of thecantilever; measuring a lateral signal associated with a torsional modeof the cantilever during atomic force microscopy (AFM) measurements andmeasuring a vertical signal associated with relative displacement, alongthe direction, of the probe tip and the sample, wherein the lateralsignal corresponding to a force between the sample and the probe tip;and determining the information about the sample based on the lateralsignal and the vertical signal.
 30. The method of claim 29, wherein acontribution of parasitic signals to the information is reduced withoutperforming a recovery operation; wherein the parasitic signalscorresponding to phenomena other than probe tip-sample interaction andthermal noise of the cantilever and noise associated with a detectorthat measures the lateral signal; and wherein the recovery operationinvolves performing measurements when the probe tip is other than incontact with the sample.
 31. The method of claim 29, wherein theinformation includes one of: the force between the sample and the probetip, topography of the sample, and a material property of the sample.32. The method of claim 29, wherein the fundamental frequency is alesser of: the flexural resonance frequency divided by a square root oftwo, and the flexural resonance frequency times one minus an inverse oftwo times a quality factor of the flexural resonance.
 33. The method ofclaim 29, wherein a ratio of an offset of the probe tip along thelateral direction to a cantilever body length is greater than or equalto 0.235; and wherein a ratio of the offset to a cantilever body lateralwidth is greater than or equal to
 3. 34. The method of claim 29, whereinthe determination involves correcting for parasitic signals in thelateral signal and the vertical signal, the parasitic signalscorresponding to phenomena other than probe tip-sample interaction andthermal noise of the cantilever and noise associated with a detectorthat measures the lateral signal.
 35. A non-transitory computer-readablestorage medium for use in conjunction with an atomic force microscope(AFM), the computer-readable storage medium configured to store aprogram module that, when executed by the AFM, causes the AFM to: vary adistance between a sample and a probe tip along a directionapproximately perpendicular to a plane of the sample in an intermittentcontact mode, wherein the probe tip is included in a cantilever and isoffset along a lateral direction from a longitudinal axis of torsion ofthe cantilever, and wherein the variation of the distance has afundamental frequency that is significantly less than a lowest flexuralresonance frequency of the cantilever; measure a lateral signalassociated with a torsional mode of the cantilever during atomic forcemicroscopy (AFM) measurements and measure a vertical signal associatedwith relative displacement, along the direction, of the probe tip andthe sample, wherein the lateral signal corresponding to a force betweenthe sample and the probe tip; and determine information about the samplebased on the lateral signal and the vertical signal.
 36. Thecomputer-readable storage medium of claim 35, wherein a contribution ofparasitic signals to the information is reduced without performing arecovery operation; wherein the parasitic signals corresponding tophenomena other than probe tip-sample interaction and thermal noise ofthe cantilever and noise associated with a detector that measures thelateral signal; and wherein the recovery operation involves performingmeasurements when the probe tip is other than in contact with thesample.
 37. The computer-readable storage medium of claim 35, whereinthe information includes one of: the force between the sample, and theprobe tip, topography of the sample, and a material property of thesample.
 38. The computer-readable storage medium of claim 35, whereinthe fundamental frequency is a lesser of: the flexural resonancefrequency divided by a square root of two, and the flexural resonancefrequency times one minus an inverse of two times a quality factor ofthe flexural resonance.
 39. The computer-readable storage medium ofclaim 35, wherein a ratio of an offset of the probe tip along thelateral direction to a cantilever body length is greater than or equalto 0.235; and wherein a ratio of the offset to a cantilever body lateralwidth is greater than or equal to
 3. 40. The computer-readable storagemedium of claim 35, wherein the determination involves correcting forparasitic signals in the lateral signal and the vertical signal, theparasitic signals corresponding to phenomena other than probe tip-sampleinteraction and thermal noise of the cantilever and noise associatedwith a detector that measures the lateral signal.